Waves in Oceanic and Coastal Waters.pdf PDF

Preview

Summary

This page intentionally left blank Quotes from pre-publication reviews ‘This book will undoubtedly be welcomed by the extensive engineering community concerned with the impact of ocean waves on ships, off-shore structures, coastal protection, dikes, harbours, beaches and tidal basins . . . The book...

Description

This page intentionally left blank

Quotes from pre-publication reviews ‘This book will undoubtedly be welcomed by the extensive engineering community concerned with the impact of ocean waves on ships, off-shore structures, coastal protection, dikes, harbours, beaches and tidal basins . . . The book contains a trove of practical information on all aspects of waves in the open ocean and coastal regions . . . providing an invaluable source of information.’ K. Hasselmann, Director (retired) of the Max-Planck-Institut f¨ur Meteorologie, Hamburg, and Emeritus Professor of Theoretical Geophysics, University of Hamburg, Germany ‘The author, well-known for his work in wave modeling and the development of the SWAN model, provides a valuable introduction to ocean wave statistics, generation by wind, and modeling in deep and shallow water. . . . The book will be very helpful to students, as well as professionals, interested in wind-wave wave modeling. All SWAN users will want a copy.’ R.A. Dalrymple, Williard & Lillian Hackerman Professor of Civil Engineering, Johns Hopkins University, USA ‘. . . the best introduction to practical engineers to grasp the directional spectral wave approach. . . . The book is excellent not only as a textbook for students but also as a reference book for professionals.’ Y. Goda, Executive Advisor to ECOH CORPORATION, Emeritus Professor of Civil Engineering, Yokohama National University, Director-General (retired) of the Port and Airport Research Institute, Japan ‘. . . ideally suited as a reference work for advanced undergraduate and graduate students and researches. . . . The book is a “must have” for engineers and scientists interested in the ocean. . . . The book explains quite complex processes with remarkable clarity and the use of informative examples. Drawing on the author’s international reputation as a researcher in the field, the book brings together classical theory and state of the art techniques in a consistent framework. It is an invaluable reference for students, researchers and practitioners.’ I. Young, Vice-Chancellor and President of Swinburne University of Technology, Australia

‘This is a great book. The author is one of the leading experts in the field of waves who has taught the subject for over 20 years – and it shows. The book has a broad scope, which would be of interest to students just learning the subject, as well as professionals who wish to broaden their range of knowledge or who want to refresh their memory . . . recommended for introductory as well as advanced students and professionals.’ J. W. Kamphuis, Emeritus Professor of Civil Engineering, Queen’s University, Canada ‘This book presents an original and refreshing view on nearly all topics which are required nowadays to deal with wind generated waves at the sea surface. . . . The logical structure . . . and the fact that it avoids complex numbers and vector notation will . . . facilitate its comprehension.’ A. S´anchez-Arcilla, Professor of Coastal Engineering, Universitat Polit`ecnica de Catalunya, Spain ‘. . . highlights key concepts, unites seemingly unconnected theories, and unlocks the complexity of the sea. [This book] will become an important reference for students, coastal and ocean engineers, and oceanographers.’ J. Smith, Editor, International Conference on Coastal Engineering, US Army Engineer Research and Development Center, USA ‘. . . Although several books on waves already exist, I find this new contribution particularly valuable . . . I will thus particularly recommend [it] for people wishing to acquire and understand the key-concepts and essential notions on waves in oceanic and coastal waters.’ M. Benoit, Research Engineer, Laboratoire National d’Hydraulique, France ‘This book is exceptionally well organized for teachers who want a thorough introduction to ocean waves in nature. It fills a key gap in text books, between overly simplistic treatments of ocean waves and detailed theoretical/mathematical treatises beyond the needs of most students. I found the text very clear and readable. Explanations and derivations within this book are both innovative and instructive and the focus on key elements required to build a strong foundation in ocean waves remains strong throughout the book.’ D. T. Resio, Chief Research and Development Advisor, US Army Engineer Research & Development Center, USA

WAV ES IN O C EA N IC A N D COAS TAL WAT E RS

Waves in Oceanic and Coastal Waters describes the observation, analysis and prediction of wind-generated waves in the open ocean, in shelf seas, and in coastal regions. The book brings graduate students, researchers and engineers up-to-date with the science and technology involved, assuming only a basic understanding of physics, mathematics and statistics. Most of this richly illustrated book is devoted to the physical aspects of waves. After introducing observation techniques for waves, both at sea and from space, the book defines the parameters that characterize waves. Using basic statistical and physical concepts, the author discusses the prediction of waves in oceanic and coastal waters, first in terms of generalized observations, and then in terms of the more theoretical framework of the spectral energy balance: their origin (generation by wind), their transformation to swell (dispersion), their propagation into coastal waters (shoaling, refraction, diffraction and reflection), the interaction amongst themselves (wave-wave interactions) and their decay (white-capping, bottom friction, and surf-breaking). He gives the results of established theories and also the direction in which research is developing. The book ends with a description of SWAN (Simulating Waves Nearshore), the preferred computer model of the engineering community for predicting waves in coastal waters.

Early in his career, the author was involved in the development of techniques to measure the directional characteristics of wind-generated waves in the open sea. He contributed to various projects, in particular the Joint North Sea Wave Project (JONSWAP), which laid the scientific foundation for modern wave prediction. Later, he concentrated on advanced research and development for operational wave prediction and was thus involved in the initial development of the computer models currently used for global wave prediction at many oceanographic and meteorological institutes in the world. More recently, he initiated, supervised and co-authored SWAN, the computer model referred to above, for predicting waves in coastal waters. For ten years he co-chaired the Waves in Shallow Environments (WISE) group, a world wide forum for research and development underlying operational wave prediction. He has published widely on the subject and teaches at the Delft University of Technology and UNESCO-IHE in the Netherlands.

WAVE S IN OCE A NI C AND COASTAL WAT E R S L E O H . H O LT H U I J S E N Delft University of Technology and UNESCO-IHE

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521860284 © L. H. Holthuijsen 2007 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2007 ISBN-13 ISBN-10

978-0-511-27021-5 eBook (NetLibrary) 0-511-27021-6 eBook (NetLibrary)

ISBN-13 ISBN-10

978-0-521-86028-4 hardback 0-521-86028-8 hardback

Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

Contents

Preface Acknowledgements

page xiii xv

1 Introduction 1.1 Key concepts 1.2 This book and its reader 1.3 Physical aspects and scales 1.4 The structure of the book

1 1 1 3 7

2 Observation techniques 2.1 Key concepts 2.2 Introduction 2.3 In situ techniques 2.3.1 Wave buoys 2.3.2 Wave poles 2.3.3 Other in situ techniques 2.4 Remote-sensing techniques 2.4.1 Imaging techniques Stereo-photography Imaging and non-imaging radar 2.4.2 Altimetry Laser altimetry Acoustic altimetry Radar altimetry

10 10 10 12 13 15 17 18 19 19 20 21 21 22 22

3 Description of ocean waves 3.1 Key concepts 3.2 Introduction 3.3 Wave height and period 3.3.1 Waves 3.3.2 Wave height 3.3.3 Wave period

24 24 24 25 25 27 29

vii

viii

Contents

3.4 Visual observations and instrumental measurements 3.5 The wave spectrum 3.5.1 Introduction 3.5.2 The random-phase/amplitude model 3.5.3 The variance density spectrum 3.5.4 Interpretation of the variance density spectrum 3.5.5 Alternative definitions The spectral domain Formal definition 3.5.6 The frequency–direction spectrum 3.5.7 The spectrum at sea 3.5.8 Wave-number spectra The one-dimensional wave-number spectrum The two-dimensional wave-number spectrum The three-dimensional frequency–wave-number spectrum 3.5.9 Spectrum acquisition 3.6 Transfer functions and response spectra

29 31 31 33 36 38 41 41 42 43 47 48 49 49 50 51 52

4 Statistics 4.1 Key concepts 4.2 Short-term statistics 4.2.1 Instantaneous surface elevation 4.2.2 Wave height and period Wave period Crest height Wave height 4.2.3 Wave groups 4.2.4 Extreme values Extreme elevations Extreme wave heights 4.3 Long-term statistics (wave climate) 4.3.1 The initial-distribution approach 4.3.2 The peak-over-threshold approach 4.3.3 The annual-maximum approach 4.3.4 Individual wave height 4.3.5 Wave atlases

56 56 56 57 60 60 62 68 75 77 78 82 85 87 95 98 101 105

5 Linear wave theory (oceanic waters) 5.1 Key concepts 5.2 Introduction

106 106 107

Contents

ix

5.3 Basic equations and boundary conditions 5.3.1 Idealisations of the water and its motions 5.3.2 Balance equations Mass balance and continuity equations Momentum balance 5.3.3 Boundary conditions 5.3.4 The velocity potential function 5.4 Propagating harmonic wave 5.4.1 Introduction 5.4.2 Kinematics Particle velocity Particle path 5.4.3 Dynamics The dispersion relationship Phase velocity and group velocity Wave-induced pressure 5.4.4 Capillary waves 5.5 Wave energy (transport) 5.5.1 Wave energy 5.5.2 Energy transport 5.6 Nonlinear, permanent waves 5.6.1 Introduction 5.6.2 Stokes’ theory and Dean’s stream-function theory 5.6.3 Cnoidal and solitary waves

107 108 109 112 112 114 115 118 118 119 120 121 123 123 125 128 129 131 131 132 137 137 139 142

6 Waves in oceanic waters 6.1 Key concepts 6.2 Introduction 6.3 Wave modelling for idealised cases (oceanic waters) 6.3.1 Idealised wind 6.3.2 The significant wave 6.3.3 The one-dimensional wave spectrum 6.3.4 The two-dimensional wave spectrum 6.4 Wave modelling for arbitrary cases (oceanic waters) 6.4.1 The energy balance equation 6.4.2 Wave propagation and swell 6.4.3 Generation by wind 6.4.4 Nonlinear wave–wave interactions (quadruplet) 6.4.5 Dissipation (white-capping) 6.4.6 Energy flow in the spectrum 6.4.7 First-, second- and third-generation wave models

145 145 146 147 148 150 155 162 167 169 174 177 183 188 192 194

x

Contents

7 Linear wave theory (coastal waters) 7.1 Key concepts 7.2 Introduction 7.3 Propagation 7.3.1 Shoaling 7.3.2 Refraction 7.3.3 Diffraction 7.3.4 Refraction and diffraction 7.3.5 Tides and currents 7.3.6 Reflections 7.4 Wave-induced set-up and currents 7.4.1 Introduction 7.4.2 Wave momentum and radiation stress 7.4.3 Wave-induced set-up, set-down and currents 7.5 Nonlinear, evolving waves 7.5.1 Introduction 7.5.2 The Boussinesq model 7.6 Breaking waves

197 197 197 199 199 202 210 217 218 221 225 225 225 234 239 239 240 242

8 Waves in coastal waters 8.1 Key concepts 8.2 Introduction 8.3 Wave modelling for idealised cases (coastal waters) 8.3.1 The significant wave 8.3.2 The one-dimensional wave spectrum 8.3.3 The two-dimensional wave spectrum 8.4 Wave modelling for arbitrary cases (coastal waters) 8.4.1 The energy/action balance equation 8.4.2 Wave propagation 8.4.3 Generation by wind 8.4.4 Nonlinear wave–wave interactions Quadruplet wave–wave interactions Triad wave–wave interactions 8.4.5 Dissipation White-capping Bottom friction Depth-induced (surf-)breaking 8.4.6 Energy flow in the spectrum

244 244 245 246 247 250 256 256 257 263 268 269 269 270 276 276 276 281 284

Contents

xi

9 The SWAN wave model 9.1 Key concepts 9.2 Introduction 9.3 Action balance 9.3.1 The action balance equation 9.3.2 Generation by wind 9.3.3 Nonlinear wave–wave interactions Quadruplet wave–wave interactions Triad wave–wave interactions 9.3.4 Dissipation White-capping Bottom friction Depth-induced (surf-)breaking Reflection, transmission and absorption 9.4 Wave-induced set-up 9.5 Numerical techniques 9.5.1 Introduction 9.5.2 Propagation Numerical schemes Solvers, grids and boundaries 9.5.3 Generation, wave–wave interactions and dissipation Positive source terms Negative source terms Numerical stability 9.5.4 Wave-induced set-up

286 286 286 288 288 289 292 292 293 294 294 295 296 296 296 298 298 299 301 305 306 307 307 308 309

Appendix A Appendix B Appendix C Appendix D Appendix E References Index

310 318 324 335 342 347 379

Random variables Linear wave theory Spectral analysis Tides and currents Shallow-water equations

Preface

In my position as associate professor at Delft University of Technology and as a guest lecturer at UNESCO-IHE (Delft, the Netherlands), I have for more than 20 years, with great pleasure, supported students and professionals in their study of ocean waves. At Delft University I have had, in addition, the opportunity to work with colleagues, notably Nico Booij, on developing numerical wave models, one of which (SWAN) has widely been accepted as an operational model for predicting waves in coastal waters. Over the years, I have made notes to assist these professionals, students and myself, during courses, workshops and training sessions. With the growing interest and willingness of others to formalise these (mostly handwritten) notes, I found that I should make the effort myself. The result is this book Waves in Oceanic and Coastal Waters, which provides an introduction to the observation, analysis and prediction of wind-generated waves in the open ocean, in shelf seas and in coastal regions. The title of the book is a little prosaic because I want to focus directly on the subject matter of the book. A more poetic title would be Waves of The Blue Yonder, which would convey better the awe and mystery that I feel when watching waves at sea, wondering where they come from and what they have seen on their journey across the oceans. The cover photo illustrates this feeling beautifully. Understanding the text of the book requires some basic knowledge of physics, mathematics and statistics. The text on observing waves (Chapter 2) is descriptive; no mathematics or statistics is used. Understanding the text on describing ocean waves (Chapters 3 and 4) does require some knowledge of mathematics and statistics, since concepts of analytical integration and probabilities are used. The text on the linear theory of surface gravity waves (Chapters 5 and 7) and the text on modelling wind-generated waves (Chapters 6 and 8) rely heavily on the concepts of conservation of mass, momentum and energy. Therefore, some background in physics is needed. These concepts are expressed with partial differential equations, so some background in mathematics is also needed. Finally, the book ends in Chapter 9 with a description of the fundamentals of SWAN (both its physical principles and numerical techniques). I first treat waves in oceanic waters and later in coastal waters. The reason for this separation is both didactic and practical: the physical processes increase in number

xiii

xiv

Preface

and complexity as waves move from the ocean into coastal waters. Describing waves in the oceans therefore gives a good introduction to the more challenging subject of waves in coastal waters. In addition, many readers will be interested only in the ocean environment and need not be bothered with the coastal environment. I am well aware that many formulations in this book can be written in vector or complex notation. Such notation would make for compact reading for those who are familiar with it. However, students who are not familiar with it would not readily absorb the material presented, so I have chosen not to use it. With a few exceptions, I have written in terms of components rather than vectors and real quantities rather than complex quantities. Concerning the references in the book: I have used a fair number of these, to (a) refer to specific information, (b) indicate where issues are being discussed and (c) refer to books and articles for further reading. I have not tried to be complete in this. That would be nearly impossible, if only because of the continual appearance of new publications. Moreover, any subject is accessible on the Internet, which is completely up to date, including electronic versions of scientific and engineering journals. If this book helps professionals to enjoy their work more, students to pursue their interest in waves and others to look at waves with an informed eye, it has more than served its purpose. L. H. Holthuijsen, Delft

Acknowledgements

I was supported in writing this book by three close friends and colleagues: Luigi Cavaleri of the Istituto di Scienze Marine in Venice (Italy), whom I visited so often (memories of Venice waking up in the early morning sunlight, when it is still a cool and quiet place); Masataka Yamaguchi of the Ehime University in Matsuyama (Japan), who introduced me to the many charms of Japan (memories of the mountains and quiet villages along the rugged Pacific coast of his home island Shikoku); and Nico Booij, with whom I shared, almost daily, my professional enthusiasm, ideas and dreams in such diverse places as Delft, Reykjav´ık and Beijing. They read the book from cover to cover (and back, more than once) and they gave their comments and suggestions freely. This was not a trivial effort. They saved me from embarrassing errors and helped achieve a balance between scope, reliability and accessibility on the one hand and detail, accuracy and formalism on the other. I am very grateful to them and I am proud that they are my friends, and have been for 25 years now. I also want to thank Linwood Vincent of the US Office of Naval Research, whose inspiring words encouraged me to write this book. In addition, I have had the privilege to be assisted by several colleagues with specific information, in particular on the subject of wave statistics: Akira Kimura of the University of Tottori, Japan; Evert Bouws and Sofia Caires of the Royal Netherlands Meteorological Institute; Ulla Machado of Oceanor, Norway; Sverre Haver of Statoil, Norway; Agnieszka Herman of the Lower Saxonian Central State Board for Ecology in Norderney, Germany; and Pieter van Gelder, Andr´e van der Westhuysen and Marcel Zijlema of the Delft University of Technology. Mrs. Paula Delhez and her colleagues of the Delft University Library helped me find the references in this book. I am very grateful to all of them because their help greatly improved the quality of the book. Still, any errors that are left (and fate dictates that some will be) are wholly mine. In the book I have used data provided by the Royal Netherlands Meteorological Institute (the Netherlands), Fugro Oceanor AS (Norway), the National Oceanic and Atmospheric Administration (USA) ...